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This scale occurs in 12edo, where it is the equal division of the minor ninth. It has the Grandfather 5L 3s MOS with a 2:1 ratio of large against small.
This scale, a Long Common Practice minor mode, occurs in 12edo; where it is the equal division of the minor ninth. It has the Grandfather 5L 3s MOS with a 2:1 ratio of large against small.
==Tuning spectrum==
==Tuning spectrum==
{| class="wikitable"
{| class="wikitable"
|+
! rowspan="2" |Degrees
! colspan="5" rowspan="2" |Period
! rowspan="2" |Octatonic
! colspan="5" |Octatonic (5L 3s)
! colspan="15" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
! rowspan="2" |Notes
|-
|-
!L
!Absolute Minimum
!s
!5ed(21/16)
! colspan="3" |Tetrachord
! |Minimum
!4ed(5/4)
!10ed(7/4)
! |Golden
!7ed(40/27)
!<nowiki><-1\4 -1\18 13\72|</nowiki>
! |Median
!9ed(5/3)
!14ed(20/9)
! |Mean
! |5ed(4/3)
!7edf
! |Maximum
|-
|-
|1\1edo
| |1
|
| |F#/Gb
|
|
|
|184.615
|92.308
|92.308
|94.156
| |96
|96.578
|96.883
| |97.098
|97.207
|97.42
| |97.582
|98.262
|98.743
| |98.769
| |99.609
|100.279
| |101.5385
|-
| |2
| |G
|184.615
|184.615
|369.231
|188.312
|461.5385
| |192
|Phrygian Mode (aka Double) Neapolitan Temperament from here …
|193.157
|193.765
| |194.196
|194.414
|194.8405
| |195.164
|196.524
|197.486
| |197.5385
| |199.218
|200.559
| |203.077
|-
|-
|
| |3
|
| |G#/Ab
|
|276.923
|
|282.469
|15\14
| |288
|197.802
|289.735
|98.901
|290.648
|197.802
| |291.293
|395.604
|291.621
|494.5055
|292.261
|
| |292.747
|294.786
|286.229
| |296.308
| |298.827
|300.837
| |304.615
|-
|-
|
| |4
|
| |A
|
|369.231
|14\13
|376.625
|
| |384
|198.817
|386.314
|99.408
|387.53
|198.817
| |388.391
|397.633
|338.828
|497.041
|389.681
|
| |390.329
|393.048
|394.9725
| |395.076
| |398.436
|401.117
| |406.154
|-
|-
|
| |5
|
| |B
|
|461.5385
|
|470.781
|27\25
| |480
|199.385
|482.892
|99.692
|484.413
|199.385
| |485.489
|398.769
|486.035
|498.4615
|487.101
|
| |487.912
|491.31
|493.716
| |493.846
| |498.045
|501.396
| |507.692
|-
|-
|
| |6
|
| |B#/Hb
|13\12
|553.846
|
|564.937
|
| |576
|200
|579.471
|100
|581.2955
|200
| |582.587
|400
|583.242
|500
|584.5215
|
| |585.4945
|589.5725
|592.459
| |592.615
| |597.654
|601.676
| |609.231
|-
|-
|
| |7
|
| |H
|
|646.154
|
|659.093
|38\35
| |672
|200.44
|676.049
|100.22
|678.178
|200.44
| |679.685
|400.879
|680.448
|501.099
|681.942
|
| |683.077
|687.835
|691.202
| |691.385
| |697.263
|701.955
| |710.769
|-
|-
|
| |8
|
| |C
|
|738.4615
|25\23
|753.2495
|
| |768
|200.669
|772.627
|100.334
|775.06
|200.669
| |776.782
|401.338
|777.656
|501.672
|779.362
|
| |780.659
|786.097
|789.945
| |790.154
| |796.872
|802.234
| |812.308
|-
|-
|
| |9
|
| |C#/Db
|
|830.769
|
|847.406
|37\34
| |864
|200.905
|869.206
|100.4525
|871.943
|200.905
| |873.880
|401.81
|874.862
|502.262
|876.782
|
| |878.242
|884.359
|888.688
| |888.923
| |896.481
|902.514
| |913.846
|-
|-
|
| |10
|12\11
| |D
|
|923.077
|
|941.562
|
| |960
|201.399
|965.784
|100.699
|968.826
|201.399
| |970.978
|402.797
|972.07
|503.4965
|974.2025
|
| |975.824
|982.621
|987.431
| |987.692
| |996.09
|1002.793
| |1015.385
|-
|-
|
| |11
|
| |D#/Eb
|
|1015.385
|
|1035.718
|47\43
| |1056
|201.789
|1062.363
|100.8945
|1065.7085
|201.789
| |1068.076
|403.578
|1069.277
|504.472
|1071.623
|
| |1073.407
|1080.882
|1086.174
| |1086.4615
| |1095.699
|1103.072
| |1116.923
|-
|-
|
| |12
|
| |E
|
|1107.692
|35\32
|1129.874
|
| |1152
|201.923
|1158.941
|100.9615
|1162.591
|201.923
| |1165.1735
|403.846
|1166.4835
|504.808
|1169.043
|
| |1170.989
|1179.145
|1184.9175
| |1185.231
| |1195.308
|1203.3514
| |1218.4615
|-
|-
|
| |13
|
| |F
|
|1200
|
|1224.03
|58\53
| |1248
|202.032
|1255.52
|101.016
|1259.474
|202.032
| |1262.271
|404.064
|1263.6905
|505.08
|1266.463
|
| |1268.286
|1277.407
|1283.661
| |1284
| |1294.916
|1303.631
| |1320
|}
{| class="wikitable"
! rowspan="2" |Degrees
! rowspan="2" |Octatonic
! colspan="14" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
|-
|-
|
! |Minimum
|
!8ed(8/5)
|23\21
!10ed(9/5)
|
! |2ed(9/8)
|
!14ed(16/7)
|202.198
! |Golden
|101.099
!<nowiki><17/48 1/6 -11/48|</nowiki>
|202.198
! |Mean
|404.396
!5ed(27/20)
|505.4945
!7ed(32/21)
|
!4ed(14/11)
! |Median
!3ed(6/5)
! |Maximum
|-
|-
|
| |1
|
| |F#/Gb
|
| |101.5385
|
|101.711
|57\52
|101.76
|202.367
| |101.955
|101.183
|102.227
|202.367
| |102.733
|404.734
|103.462
|505.917
| |103.5165
|
|103.91
|104.174
|104.377
| |104.615
|105.213
| |105.4945
|-
|-
|
| |2
|
| |G
|
| |203.077
|34\31
|203.422
|
|203.519
|202.481
| |203.91
|101.241
|204.453
|202.481
| |205.466
|404.963
|206.9245
|506.2035
| |207.033
|
|207.8205
|208.348
|208.754
| |209.231
|210.4275
| |210.989
|-
|-
|
| |3
|
| |G#/Ab
|
| |304.615
|
|305.132
|45\41
|305.279
|202.627
| |305.865
|101.313
|306.68
|202.627
| |308.199
|405.253
|310.387
|506.567
| |310.5465
|
|311.731
|312.5225
|313.131
| |313.846
|315.641
| |316.4835
|-
|-
|11\10
| |4
|
| |A
|
| |406.154
|
|406.843
|
|407.0385
|203.077
| |407.82
|101.5385
|408.907
|203.077
| |410.932
|406.154
|413.849
|507.692
| |414.066
|…to here
|415.641
Phrygian-Aeolian Mode Neapolitan Temperament from here …
|416.697
|417.508
| |418.4615
|420.855
| |421.978
|-
|-
|
| |5
|
| |B
|
| |507.692
|
|508.554
|54\49
|508.798
|203.454
| |509.775
|101.757
|511.134
|203.454
| |513.6655
|406.907
|517.311
|508.634
| |517.582
|
|519.551
|520.871
|521.885
| |523.077
|526.069
| |527.4725
|-
|-
|
| |6
|
| |B#/Hb
|
| |609.231
|43\39
|610.265
|
|610.558
|203.55
| |611.73
|101.775
|613.36
|203.55
| |616.399
|407.101
|620.774
|508.876
| |621.099
|
|623.4615
|625.045
|626.262
| |627.692
|631.283
| |632.967
|-
|-
|
| |7
|
| |H
|
| |710.769
|
|711.976
|75\68
|712.317
|203.62
| |713.685
|101.81
|715.587
|203.62
| |719.132
|407.24
|724.236
|509.05
| |724.615
|
|727.372
|729.219
|730.639
| |732.318
|736.496
| |738.4615
|-
|-
|
| |8
|
| |C
|32\29
| |812.308
|
|813.686
|
|814.077
|203.7135
| |815.64
|101.857
|817.814
|203.7135
| |821.865
|407.427
|827.698
|509.284
| |828.132
|
|831.282
|833.393
|835.016
| |836.923
|841.71
| |843.856
|-
|-
|
| |9
|
| |C#/Db
|
| |913.846
|
|915.397
|85\77
|915.837
|203.796
| |917.595
|101.898
|920.041
|203.796
| |924.598
|407.592
|931.1605
|509.4905
| |931.648
|
|935.192
|937.567
|939.393
| |941.5385
|946.924
| |949.4505
|-
|-
|
| |10
|
| |D
|
| |1015.385
|53\48
|1017.108
|
|1017.596
|203.846
| |1019.55
|101.923
|1022.267
|203.846
| |1027.331
|407.692
|1034.623
|509.615
| |1035.165
|
|1039.103
|1041.742
|1043.77
| |1046.154
|1052.138
| |1054.945
|-
|-
|
| |11
|
| |D#/Eb
|
| |1116.923
|
|1118.819
|74\67
|1119.356
|203.904
| |1121.505
|101.952
|1124.494
|203.904
| |1130.064
|407.807
|1138.085
|509.759
| |1138.681
|Square root of 9/8 is near here
|1143.013
|1145.916
|1148.147
| |1150.769
|1157.351
| |1160.44
|-
|-
|
| |12
|21\19
| |E
|
| |1218.4615
|
|1220.529
|
|1221.1155
|204.049
| |1223.46
|102.024
|1226.721
|204.049
| |1232.797
|408.097
|1241.547
|510.1215
| |1242.198
|
|1246.923
|1250.09
|1252.524
| |1255.385
|1262.565
| |1265.9348
|-
|-
|
| |13
|
| |F
|
| |1320
|
|1322.24
|73\66
|1322.875
|204.196
| |1325.415
|102.098
|1238.947
|204.196
| |1335.53
|408.392
|1345.0095
|510.4895
| |1345.714
|
|1350.833
|-
|1354.264
|
|1356.901
|
| |1360
|
|1367.779
|52\47
| |1371.429
|
|}
|204.255
{| class="wikitable"
|102.128
! rowspan="2" |Degrees
|204.255
! rowspan="2" |Octatonic
|408.511
! colspan="11" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
|510.638
|
|-
|
|
|
|
|83\75
|204.308
|102.154
|204.308
|409.615
|510.769
|
|-
|
|
|31\28
|
|
|204.396
|102.198
|204.396
|408.792
|510.989
|
|-
|
|
|
|
|72\65
|204.497
|102.248
|204.497
|408.994
|511.242
|
|-
|
|
|
|41\37
|
|204.574
|102.287
|204.574
|409.148
|511.4345
|
|-
|
|
|
|
|51\46
|204.682
|102.341
|204.682
|409.3645
|511.706
|
|-
|10\9
|
|
|
|
|205.128
|102.564
|205.128
|410.256
|512.8205
|
|-
|
|
|
|
|49\44
|205.594
|102.797
|205.594
|411.189
|513.986
|
|-
|
|
|
|39\35
|
|205.714
|102.857
|205.714
|411.429
|514.286
|
|-
|-
|
! |Minimum
|
!ed(20/9)
|
! |Golden
|
! |Median
|68\61
!9ed(5/3)
|205.801
! |ed(9/4)
|102.9
! |Mean
|205.801
!4ed(9/7)
|411.6015
!26ed(36/7)
|514.502
!ed(16/7)
|
! |Maximum
|-
|-
|
| |1
|
| |F#/Gb
|29\26
| |105.4945
|
|106.339
|
| |107.11
|205.917
| |107.692
|102.959
|98.262
|205.917
| |107.993
|411.824
| |108.132
|514.799
|108.771
|
|109.042
|110.09
| |110.769
|-
|-
|
| |2
|
| |G
|
| |210.989
|
|212.6775
|77\69
| |214.22
|206.02
| |214.385
|103.01
|196.524
|206.02
| |215.986
|412.04
| |216.264
|515.05
|217.542
|
|218.083
|220.181
| |221.5385
|-
|-
|
| |3
|
| |G#/Ab
|
| |304.615
|48\43
|319.016
|
| |321.33
|206.082
| |322.077
|103.041
|294.786
|206.082
| |323.979
|412.165
| |324.396
|515.205
|326.313
|
|327.125
|330.271
| |332.308
|-
|-
|
| |4
|
| |A
|
| |421.978
|
|425.355
|67\60
| |428.44
|206.154
| |429.769
|103.077
|393.048
|206.154
| |431.972
|412.308
| |432.5275
|515.385
|435.084
|
|436.167
|440.361
| |443.076
|-
|-
|
| |5
|19\17
| |B
|
| |527.4725
|
|531.694
|
| |535.55
|206.335
| |583.4615
|103.167
|491.31
|206.335
| |539.965
|412.67
| |540.659
|515.837
|543.855
|
|545.2085
|550.452
| |553.846
|-
|-
|
| |6
|
| |B#/Hb
|
| |609.231
|
|638.0325
|66\59
| |642.6595
|206.519
| |646.154
|103.2595
|589.5725
|206.519
| |647.9585
|413.038
| |648.791
|516.297
|652.626
|
|654.25
|660.542
| |664.615
|-
|-
|
| |7
|
| |H
|
| |710.769
|47\42
|744.371
|
| |749.769
|206.593
| |753.846
|103.297
|687.835
|206.593
| |755.9515
|413.187
| |756.923
|516.4835
|761.397
|
|863.292
|770.632
| |775.385
|-
|-
|
| |8
|
| |C
|
| |812.308
|
|850.71
|75\67
| |856.879
|206.659
| |861.5385
|103.3295
|786.097
|206.659
| |863.945
|413.318
| |865.055
|516.6475
|870.168
|
|872.334
|880.7225
| |886.154
|-
|-
|
| |9
|
| |C#/Db
|28\25
| |913.846
|
|957.049
|
| |963.989
|206.769
| |969.231
|103.385
|884.359
|206.769
| |971.938
|413.5385
| |973.187
|516.923
|978.939
|
|981.375
|990.813
| |996.923
|-
|-
|
| |10
|
| |D
|
| |1015.385
|
|1063.3875
|65\58
| |1071.099
|206.897
| |1076.923
|103.443
|982.621
|206.897
| |1079.931
|413.793
| |1081.319
|517.241
|1087.71
|
|1090.416
|1100.903
| |1107.692
|-
|-
|
| |11
|
| |D#/Eb
|
| |1116.923
|37\33
|1169.726
|
| |1178.209
|206.993
| |1184.615
|103.4965
|1080.882
|206.993
| |1187.924
|413.986
| |1189.4505
|517.4825
|1196.481
|
|1199.459
|1210.9935
| |1218.4615
|-
|-
|
| |12
|
| |E
|
| |1218.4615
|
|1276.065
|46\41
| |1285.319
|207.1295
| |1292.308
|103.565
|1179.145
|207.1295
| |1295.917
|414.259
| |1297.582
|517.824
|1305.252
|
|1308.5
|1321.084
| |1329.231
|-
|-
|9\8
| |13
|
| |F
|
| |1371.429
|
|1382.403
|
| |1392.429
|207.692
| |1400
|103.846
|1277.407
|207.692
| |1403.91
|415.385
| |1405.714
|519.231
|1414.023
|
|1417.524
|-
|1431.174
|
| |1440
|
|
|
|44\39
|208.284
|104.142
|208.284
|416.568
|520.71
|
|-
|
|
|
|35\31
|
|208.437
|104.218
|208.437
|416.873
|521.092
|
|-
|
|
|
|
|61\54
|208.547
|104.2735
|208.547
|417.094
|521.3675
|
|-
|
|
|26\23
|
|
|208.696
|104.348
|208.696
|417.391
|521.739
|
|-
|
|
|
|
|69\61
|208.827
|104.414
|208.827
|417.6545
|522.068
|
|-
|
|
|
|43\38
|
|208.907
|104.453
|208.907
|417.814
|522.267
|
|-
|
|
|
|
|60\53
|208.9985
|104.499
|208.9985
|417.997
|522.496
|
|-
|
|17\15
|
|
|
|209.231
|104.615
|209.231
|418.4615
|523.077
|
|-
|
|
|
|
|59\52
|209.4675
|104.734
|209.4675
|418.935
|523.669
|
|-
|
|
|
|42\37
|
|209.563
|104.782
|209.563
|419.127
|523.9085
|
|-
|
|
|
|
|67\59
|209.648
|104.824
|209.648
|419.296
|524.12
|
|-
|
|
|25\22
|
|
|209.79
|104.895
|209.79
|419.58
|524.4755
|
|-
|
|
|
|
|58\51
|209.955
|104.977
|209.955
|419.91
|524.887
|
|-
|
|
|
|33\29
|
|210.08
|105.04
|210.08
|420.159
|525.199
|
|-
|
|
|
|
|41\36
|210.256
|105.128
|210.256
|420.513
|525.641
|
|-
|8\7
|
|
|
|
|210.989
|105.4945
|210.989
|421.978
|527.4725
|…to here
Aeolian Mode Neapolitan Temperament from here …
|-
|
|
|
|
|39\34
|211.765
|105.882
|211.765
|423.529
|529.412
|
|-
|
|
|
|31\27
|
|211.966
|105.983
|211.966
|423.932
|529.9145
|
|-
|
|
|
|
|54\47
|212.111
|106.056
|212.111
|424.223
|530.278
|
|-
|
|
|23\20
|
|
|212.308
|106.154
|212.308
|424.615
|530.769
|
|-
|
|
|
|
|61\53
|212.482
|106.241
|212.482
|424.964
|531.205
|
|-
|
|
|
|38\33
|
|212.587
|106.294
|212.587
|425.175
|531.4685
|
|-
|
|
|
|
|53\46
|212.709
|106.3595
|212.709
|425.418
|531.773
|
|-
|
|15\13
|
|
|
|213.018
|106.509
|213.018
|426.0355
|532.544
|
|-
|
|
|
|
|52\45
|213.333
|106.667
|213.333
|426.667
|533.333
|
|-
|
|
|
|37\32
|
|213.4615
|106.731
|213.4615
|426.923
|533.654
|
|-
|
|
|
|
|59\51
|213.575
|106.787
|213.575
|427.149
|533.937
|
|-
|
|
|22\19
|
|
|213.765
|106.883
|213.765
|427.52
|534.413
|
|-
|
|
|
|
|51\44
|213.986
|106.993
|213.986
|427.972
|534.965
|
|-
|
|
|
|29\25
|
|214.154
|107.077
|214.154
|428.308
|535.385
|
|-
|
|
|
|
|36\31
|214.392
|107.196
|214.392
|428.784
|535.98
|
|-
|7\6
|
|
|
|
|215.385
|107.692
|215.385
|430.769
|538.4615
|
|-
|
|
|
|
|34\29
|216.446
|108.223
|216.446
|432.891
|541.114
|
|-
|
|
|
|27\23
|
|216.722
|108.361
|216.722
|433.445
|541.806
|
|-
|
|
|
|
|47\40
|216.923
|108.4615
|216.923
|433.846
|542.308
|
|-
|
|
|20\17
|
|
|217.195
|108.597
|217.195
|434.389
|542.986
|
|-
|
|
|
|
|53\45
|217.436
|108.718
|217.436
|434.872
|543.59
|
|-
|
|
|
|33\28
|
|217.582
|108.791
|217.582
|435.165
|543.956
|
|-
|
|
|
|
|46\39
|217.7515
|108.876
|217.7515
|435.503
|544.679
|
|-
|
|13\11
|
|
|
|218.182
|109.091
|218.182
|436.364
|545.4545
|
|-
|
|
|
|
|45\38
|218.6235
|109.312
|218.6235
|437.247
|546.5559
|
|-
|
|
|
|32\27
|
|218.803
|109.402
|218.803
|437.606
|547.0085
|
|-
|
|
|
|
|51\43
|218.962
|109.461
|218.962
|406.6445
|547.406
|
|-
|
|
|19\16
|
|
|219.231
|109.615
|219.231
|438.4615
|548.077
|
|-
|
|
|
|
|44\37
|219.543
|109.771
|219.543
|439.085
|548.8565
|
|-
|
|
|
|25\21
|
|219.78
|109.89
|219.78
|439.56
|549.4505
|
|-
|
|
|
|
|31\26
|220.118
|110.059
|220.118
|440.237
|550.296
|
|-
|6\5
|
|
|
|
|221.5385
|110.769
|221.5385
|443.077
|553.846
|…to here
|}
|}
[[Category:13-tone]]
[[Category:13-tone]]
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/13edIX"